Equilibrium Structure and Radial Oscillations of Dark Matter Admixed Neutron Stars

In [Leung et al., Phys. Rev. D 84, 107301 (2011)], we presented our results on using a general relativistic two-fluid formalism to study the hydrostatic equilibrium configuration of an admixture of degenerate dark matter and normal nuclear matter. In this work, we present more analysis to complement our previous findings. We study the radial oscillation modes of these compact stars in detail. We find that these stars in general have two classes of oscillation modes. For a given total mass of the star, the first class of modes is insensitive to the dark-matter particle mass. They also reduce properly to the oscillation modes of the corresponding ordinary neutron star, with the same total mass, when the mass fraction of dark matter tends to zero. On the other hand, the second class of modes is due mainly to the dark-matter fluid. In the small dark-matter mass fraction limit, these modes are characterized purely by the oscillations of dark matter, while the normal matter is essentially at rest. In the intermediate regime where the mass fractions of the two fluids are comparable, the normal matter oscillates with the dark matter due to their coupling through gravity. In contrast to the first class of modes, the frequencies of these dark-matter dominated modes depend sensitively on the mass of dark-matter particles.